Problem: $J$ is the midpoint of $\overline{CT}$ $C$ $J$ $T$ If: $ CJ = 3x - 1$ and $ JT = 8x - 36$ Find $CT$.
Explanation: A midpoint divides a segment into two segments with equal lengths. ${CJ} = {JT}$ Substitute in the expressions that were given for each length: $ {3x - 1} = {8x - 36}$ Solve for $x$ $ -5x = -35$ $ x = 7$ Substitute $7$ for $x$ in the expressions that were given for $CJ$ and $JT$ $ CJ = 3({7}) - 1$ $ JT = 8({7}) - 36$ $ CJ = 21 - 1$ $ JT = 56 - 36$ $ CJ = 20$ $ JT = 20$ To find the length $CT$ , add the lengths ${CJ}$ and ${JT}$ $ CT = {CJ} + {JT}$ $ CT = {20} + {20}$ $ CT = 40$